Power maps and subvarieties of the complex algebraic $n$--torus
Abstract
Description
Given a subvariety $V$ of the complex algebraic torus ${\mathbb G}_{\rm m}^n$ defined by polynomials of total degree at most $d$ and a power map $ϕ: {\mathbb G}_{\rm m}^n \to {\mathbb G}_{\rm m}^n$, the points ${\bf x}$ whose forward orbits ${\mathcal O}_ϕ({\bf x})$ belong to $V$ form its {\em stable} subvariety $S(V,ϕ)$. The main result of the paper provides an upper bound $T=T(n,d,ϕ)$ for the number of iterations of the power map $ϕ$ required to ``cut off'' the points of $V$ that do not belong to $S$.
12 pages, corrected typos
12 pages, corrected typos